I was previously given an Entei through trade. Soon after I caught Ho-oh in my own game I went to the Trackless Forest where the 3 Legendary Beasts could be caught. When I walk up to the portal it just says "A mysterious ring is floating in the air..."
Yes you can still catch all of the three dogs. But you cant have any of them in your party when you go to get the next one. So simply take entei off your team and go throu again.